Health Secretary Matt Hancock says the death of three people in a stabbing attack in Reading was a “terrible crime, whatever the motivation”.
He said it is not being treated as a terror incident but added: “We are closely monitoring the situation.”
A 25-year-old man from Reading was arrested after the attack at about 19:00 BST on Saturday, which also left three people seriously injured.
Security sources told the BBC the man arrested is thought to be Libyan.
Speaking on the BBC’s Andrew Marr Show, Mr Hancock said Home Secretary Priti Patel and Prime Minister Boris Johnson would be in contact with police leading the investigation later on Sunday.
“This is not currently being treated as a terrorist incident but we are closely monitoring the situation,” he said.
“It’s clearly a terrible crime whatever the motivation and we will be making sure the police have all the support they need.”
The prime minister met security officials, police and senior ministers at Downing Street on Sunday at 09:00 BST and was updated on the ongoing investigation.
An eyewitness to the attack at Forbury Gardens, a park near the centre of Reading, said he saw a man moving between groups of people in the park, trying to stab them.
The arrested man had previously been in prison in the UK for a relatively minor conviction, not a terrorism offence, sources told the BBC.